Control variates and importance sampling for efficient bootstrap simulations
 Tim Hesterberg
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Importance sampling and control variates have been used as variance reduction techniques for estimating bootstrap tail quantiles and moments, respectively. We adapt each method to apply to both quantiles and moments, and combine the methods to obtain variance reductions by factors from 4 to 30 in simulation examples.
We use two innovations in control variates—interpreting control variates as a reweighting method, and the implementation of control variates using the saddlepoint; the combination requires only the linear saddlepoint but applies to general statistics, and produces estimates with accuracy of order n ^{1/2} B ^{1}, where n is the sample size and B is the bootstrap sample size.
We discuss two modifications to classical importance sampling—a weighted average estimate and a mixture design distribution. These modifications make importance sampling robust and allow moments to be estimated from the same bootstrap simulation used to estimate quantiles.
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 Title
 Control variates and importance sampling for efficient bootstrap simulations
 Journal

Statistics and Computing
Volume 6, Issue 2 , pp 147157
 Cover Date
 19960601
 DOI
 10.1007/BF00162526
 Print ISSN
 09603174
 Online ISSN
 15731375
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Variance reduction
 control variates
 bootstrap
 saddlepoint
 Industry Sectors
 Authors

 Tim Hesterberg ^{(1)}
 Author Affiliations

 1. Mathematics Department, Franklin & Marshall College, 176043003, Lancaster, PA, USA